According to the 2018 Payment System Act, payment institutions and registered account information service providers from non-EU/EEA member states may not provide payment services in Croatia, unless they incorporate a payment institution in Croatia or within the territory of an EU/EEA member state. 
Under the 2018 Electronic Money Act, non-EU/EEA electronic money institutions are allowed to provide electronic money payment services associated with the issuance of electronic money in Croatia either directly or through a branch established under special
rules. Among others, a reciprocity condition applies to the establishment of a branch in Croatia in these cases. 
"Article 7
(1) Payment service providers in the Republic of Croatia may be:
1) credit institutions, in particular:
a) credit institutions established in the Republic of Croatia;
b) credit institutions established in another Member State within the meaning of Article 4, paragraph (1), item (1) of Regulation (EU) No 575/2013, including their branches within the meaning of Article 4, paragraph (1), item (17) of that Regulation when those branches are established in the Republic of Croatia;
c) third-country credit institutions through their branches established in the Republic of Croatia;
2) electronic money institutions, in particular:
a) electronic money institutions established in the Republic of Croatia;
b) electronic money institutions established in another Member State, including their branches established in the Republic of Croatia;
c) third-country electronic money institutions through their branches established in the Republic of Croatia;
3) small electronic money institutions established in the Republic of Croatia;
4) payment institutions, in particular:
a) payment institutions established in the Republic of Croatia;
b) payment institutions established in another Member State, including their branches established in the Republic of Croatia;
5) small payment institutions established in the Republic of Croatia;
6) registered account information service providers, in particular:
a) registered account information service providers established in the Republic of Croatia;
b) registered account information service providers established in another Member State, including their branches established in the Republic of Croatia;  [...]" (Payment System Act (NN 66/2018; 10 July 2018), Article 7 [unofficial translation])
-----------------------
"Article 5
(1) Electronic money issuers in the Republic of Croatia may be:
1) credit institutions, in particular:
a) credit institutions established in the Republic of Croatia;
b) credit institutions established in another Member State within the meaning of Article 4, paragraph (1), item (1) of Regulation (EU) No 575/2013, including their branches within the meaning of Article 4, paragraph (1), item (17) of that Regulation when those branches are established in the Republic of Croatia;
c) third-country credit institutions through their branches established in the Republic of Croatia;
2) electronic money institutions, in particular:
a) electronic money institutions established in the Republic of Croatia;
b) electronic money institutions established in another Member State, including their branches established in the Republic of Croatia;
c) third-country electronic money institutions through their branches established in the Republic of Croatia;
3) small electronic money institutions established in the Republic of Croatia;
[...]
Article 69
(1) A third-country electronic money institution may issue electronic money in the territory of the Republic of Croatia only through a branch.
(2) The Croatian National Bank shall be competent for issuing authorisations to establish a branch of a third-country electronic money institution. 
[...]
Article 70
(1) A third-country electronic money institution intending to issue electronic money in the Republic of Croatia, i.e. a branch of that institution, in addition to the conditions referred to in Article 16, paragraph (1), items (1), (2), (4), (6), (8) and (11) of this Act, shall also meet the following conditions: [...]
7) electronic money institutions having their head office in the Republic of Croatia are allowed to establish a branch in that third country at least under the same conditions applying to the electronic money institution establishing a branch in the Republic of Croatia; [...]" (Electronic Money Act (NN 64/2018; 10 July 2018), Articles 5, 69 and 70 [unofficial translation])
Payment System Act (NN 66/2018; 10 July 2018), Article 7 
Electronic Money Act (NN 64/2018; 10 July 2018), Articles 5, 69 and 70
[<a href="https://narodne-novine.nn.hr/clanci/sluzbeni/2018_07_66_1330.html">Act</a>],[<a href="https://www.hnb.hr/documents/20182/529405/e-payment-system-act_66-2018.pdf/b6a206ea-8279-4103-8daa-e343b6347f4d">Act_Eng</a>],[<a href="https://narodne-novine.nn.hr/clanci/sluzbeni/2018_07_64_1304.html">Act</a>],[<a href="https://www.hnb.hr/documents/20182/529405/e-electronic-money-act_64-2018.pdf/9906dc50-efef-467c-90c5-293db538b41b">Act_Eng</a>]