Ship beginning to sail with crew having little hesitation (7)
I believe the answer is:
steamer
'ship' is the definition.
(steamer is a kind of ship)
'beginning to sail with crew having little hesitation' is the wordplay.
'beginning to' indicates taking the first letters.
'with' says to put letters next to each other.
'crew' becomes 'team' (I've seen this before**).
'having' is a charade indicator (letters next to each other).
'little hesitation' becomes 'er'.
The first letter of 'sail' is 's'.
's'+'team'+'er'='STEAMER'
(Other definitions for steamer that I've seen before include "Boat; type of saucepan" , "Wetsuit" , "Large vessel - cooking vessel" , "housed in galley" , "Cooker; ship" .)