Admiral's first aboard damaged escort vessel (7)
I believe the answer is:
coaster
'vessel' is the definition.
(I've seen this before)
'admiral's first aboard damaged escort' is the wordplay.
'admiral's first' becomes 'a' (1st letter of 'admiral').
'aboard' indicates putting letters inside.
'damaged' indicates an anagram.
'escort' anagrammed gives 'coster'.
'a' put into 'coster' is 'COASTER'.
(Other definitions for coaster that I've seen before include "Tray; trader" , "Small mat; cargo ship" , "Small ship or beer mat" , "on which some mug may be made to stand?" , "Small mat for glass" .)