It would be a barrister I'd imagine, not a solicitor (for a murder case).
Can't see any conflict myself. The brief for a defense barrister is to do your best for your client. That your client is charged with the murder of a former client wouldn't affect that (to my mind). Would be a different story if the victim was a relative or friend of the accused - one wouldn't want it to seem that the barrister did anything less than his/her best.
I'd imagine that the barrister would disclose this fact to the judge but, if the client is ok with it and knows all the facts, then I don't see a problem.
The question sounds either non-hypothetical or an exam/study-related question.