Quartet aboard eastern vessel's hard to catch (7)
I believe the answer is:
evasive
'hard to catch' is the definition.
(I've seen this before)
'quartet aboard eastern vessel's' is the wordplay.
'quartet' becomes 'IV' (Roman numerals for four).
'aboard' is an insertion indicator.
'eastern' becomes 'e'.
'vessel' becomes 'vase' (vase is a kind of vessel).
'e'+'vase'='evase'
'iv' going within 'evase' is 'EVASIVE'.
(Other definitions for evasive that I've seen before include "Shifty, not direct in answering" , "Dissembling" , "Shifty and misleading" , "Prevaricatory" , "Not frank or responsive" .)