Assuming that you hold a JAA Class 1 medical and have passed all of the theoretical knowledge examinations, you will then need to pass the JAA ATPL Skill Test.
Assuming that you have a multi-pilot type (as defined by AMC-FCL 1.220) on your ICAO licence and have more than 500 hours PIC on that type then you may take the ATPL Skill Test on that type without further training. However, if you do not have the required experience on type or if you wish to take the ATPL Skill Test on a different type then you will have to complete an approved type rating training course.
This is the UK interpretation of the requirements. Other Member States may have different interpretations.