Going around primarily seeking little water bird (7)
I believe the answer is:
gosling
'water bird' is the definition.
(I know that gosling is a type of goose)
'going around primarily seeking little' is the wordplay.
'around' is an insertion indicator.
'primarily' indicates taking the first letters.
The initial letters of 'seeking little' is 'sl'.
'going' enclosing 'sl' is 'GOSLING'.
(Other definitions for gosling that I've seen before include "Young waterbird" , "Young goose" , "Little bird" , "Young bird" .)