If you really mean PSP there is in most jurisdiction no license involved or did you mean to be a acquirer?
to be a PSP you need:
anully onsite assessment trough approved QSA and quarterly network scan trough ASV.
contract with acquirer (mostly multiple to be able to cover many kind of customer business)
processing gateway (if self developed high qsa cost involved or existing certified software which is mostly not cheap)
as long you process below 300k transactions you don't need onsite assement but I don't know any acquirer that is willing to deal
regarding acquiring there is little more involved, and depends on what you exactly want to do, process payments for 3rd party, or process in name of 3rd party, and in which countries (USA too or not) and and and...
jurisdiction with benefits for european business: romania, czech republic and switzerland