Designate old hot bath no longer hot (4)
I believe the answer is:
term
'designate old' is the definition.
'term' can be an answer for 'designate' (I've seen this in another clue). I am not sure about the 'old' bit.
'hot bath no longer hot' is the wordplay.
'hot bath' becomes 'therm' (historical term for a public bath).
'no longer' suggests deleting specific letters.
'hot' becomes 'h' (abbreviation eg on taps).
'therm' with 'h' taken away is 'TERM'.
Can you help me to learn more?
(Other definitions for term that I've seen before include "A fixed or limited time - or an expression" , "Semester" , "Time in jail" , "Call" , "Part of the school year" .)