Thus live recording's beginning to get serious (5)
I believe the answer is:
sober
'serious' is the definition.
('sober' can be similar in meaning to 'serious')
'thus live recording's beginning to' is the wordplay.
'thus' becomes 'so' ('so' can be a synonym of 'thus').
'live' becomes 'be' ('be' can be a synonym of 'live').
'beginning to' indicates taking the first letters.
The initial letter of 'recordings' is 'r'.
'so'+'be'+'r'='SOBER'
'get' is the link.
(Other definitions for sober that I've seen before include "Dry - dull" , "Serious or solemn and not drunk" , "Unaffected by drink" , "Serious - sombre" , "On the wagon" .)