In short, they’re of current interest (4)
I believe the answer is:
amps
'in short they're' is the definition.
The definition suggests an adverb but the answer is not.
'current interest' is the wordplay.
'current' becomes 'amp' (electricity).
'interest' becomes 's' (I am not sure about this - if you are sure you should believe this answer much more).
'amp'+'s'='AMPS'
'of' is the link.
Can you help me to learn more?
(Other definitions for amps that I've seen before include "Current measures" , "'Units of electric current, in short (4)'" , "concert gear" , "Units of electrical power" , "Spam (anag)" .)