Time to invest in a complete coat with all haste (2,4,4)

'with all haste' is the definition.
(at full pelt means at top speed)

'time to invest in a complete coat' is the wordplay.
I cannot really understand how this works, but
'time' could be 't' (abbreviation) and 't' is found within the answer.
'a' is found in the answer.
'complete' could be 'full' (associated in meaning) and 'full' is located in the answer.
'coat' could be 'pelt' (animal coat) and 'pelt' is located in the answer.
No letters remain.
This explanation may well be incorrect...