Pair of presidents giving up British for hot secret (4-4)
I believe the answer is:
hush-hush
'secret' is the definition.
(I know that secret can be written as hush-hush)
'pair of presidents' is the wordplay.
'pair' indicates the doubling of some letters.
'of presidents' becomes 'hush' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'hush' duplicated is 'HUSH-HUSH'.
'giving up british for hot' acts as a link.
This may not be correct. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for hush-hush that I've seen before include "Be quiet, twice - it's very secret" , "Highly confidential" , "Very secret in repetitive way" , "Highly secret" , "Very secret - say it twice" .)