Could burden the old artist making return during this fiscal period (3,4)
I believe the answer is:
tax year
'during this fiscal period' is the definition.
I know nothing about this answer so I cannot tell whether this works.
'could burden the old artist making return' is the wordplay.
'could burden' becomes 'tax' (I can't explain this - if you can you should believe this answer much more).
'the old' becomes 'ye' (resembles a historical spelling of 'the').
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'making return' is a reversal indicator.
'ra' in reverse letter order is 'ar'.
'tax'+'ye'+'ar'='TAX YEAR'
Can you help me to learn more?
(Other definitions for tax year that I've seen before include "I finish on 5/4" , "I start in spring" , "It runs in the UK from the beginning of April" .)