When that dodgy pair left? (5)
I believe the answer is:
april
'when that' is the definition.
I can't judge whether this definition defines the answer.
'dodgy pair left?' is the wordplay.
'dodgy' is an anagram indicator.
'left?' becomes 'l' (common abbreviation).
'pair' anagrammed gives 'apri'.
'apri'+'l'='APRIL'
Can you help me to learn more?
(Other definitions for april that I've seen before include "Month to be in England (Browning)" , "Reputedly showery month" , "time of the year" , "Month that's autumnal in Oz" , "First month of the year with 30 days" .)