Be grateful husband's abandoned cap and jumper from the 1970s (4,3)
I believe the answer is:
tank top
'jumper from the 1970s' is the definition.
(type of jumper popular in the 1970s)
'be grateful husband's abandoned cap' is the wordplay.
'be grateful' becomes 'thank'.
'husband' becomes 'h'.
'abandoned' is a deletion indicator.
'cap' becomes 'top' (synonyms).
'thank' with 'h' taken out is 'tank'.
'tank'+'top'='TANK TOP'
'and' acts as a link.
(Other definitions for tank top that I've seen before include "that shows lots of arms?" , "Close-fitting garment" , "knitwear?" , "Young woman might appear in this" , "Sleeveless pullover" .)