As others have said, once you're qualified, that's it. The RCVS Code of Conduct requires veterinary surgeons to stick to their area of competence and refer cases where necessary, so it wouldn't be appropriate to start doing open heart surgery on day 1 of the job, but to my knowledge there are technically no additional qualifications required to do any specific procedures etc. The final year of the course is lecture-free and entirely placement-based, so we are expected to get plenty of hands on experience then.
Further education/qualification can come in the form of CPD, certificates, internships, residencies and further degrees. The latter of those tends to be for people particularly interested in academia and teaching, but is suitable for practitioners as well. Most internships and residencies require a number of years in practice as part of the entry requirements, so these tend to be to improve clinical skills and knowledge.