Family in Tiber swimming (5)
I believe the answer is:
tribe
'family' is the definition.
(I've seen this in another clue)
'tiber swimming' is the wordplay.
'swimming' is an anagram indicator.
'tiber' is an anagram of 'TRIBE'.
'in' acts as a link.
(Other definitions for tribe that I've seen before include "Group related by blood or marriage" , "Group of people with a common culture" , "Division of, eg, North American natives" , "Cultural society division" , "Race" .)