There is absolutely no requirement to have a seperate radio licence. There is no such thing under EASA, the privileges are contained within your ATPL. The UK used to issue a seperate radiotelephony licence however; that was also incorporated into the pilot licence. ICAO Annex 1 states that the radio licence may be either a seperate licence or may be incorporated into an other flight crew licence at the discretion of the NAA. The only place where reference is made to a sepearate radio licence is in the ITU General Radio Regulations Article 37 which specifies the format of a radiotelephony licence with which neither the UK nor the EASA licences comply.
If the State of Licence Issue require you to have a seperate radio licence to meet the ITU requirement then they should issue it to you on the basis of the licence you already hold.
Holders of a FAA pilot certificate must hold a FCC radiotelephony licence when operating outside the USA, something many holders do not know.