Find the answer to National Theatre becoming financially sound (7)
I believe the answer is:
solvent
'financially sound' is the definition.
(I've seen this before)
'find the answer to national theatre' is the wordplay.
'find the answer to' becomes 'solve' (I've seen this before).
'national theatre' becomes 'NT' (abbreviation).
'solve'+'nt'='SOLVENT'
'becoming' is the link.
(Other definitions for solvent that I've seen before include "not bust" , "of tradable status?" , "In credit" , "water, for example?" , "Financially viable" .)