Ships one by one leaving Spithead for short time (10)
I believe the answer is:
fleetingly
'for short time' is the definition.
(briefly or temporarily)
'ships one by one leaving spithead' is the wordplay.
'ships' becomes 'fleet' (I've seen this before).
'one by one' becomes 'singly' (synonyms).
'leaving' indicates named letters should be taken away.
'spithead' becomes 's' (head letter of 'spit').
'singly' with 's' taken away is 'ingly'.
'fleet'+'ingly'='FLEETINGLY'
(Other definitions for fleetingly that I've seen before include "momentarily" , "for a brief moment" , "for a short time" .)