In bad times, older relative's instrument (4,5)
I believe the answer is:
baby grand
'instrument' is the definition.
(baby grand is a kind of instrument)
'in bad times older relative's' is the wordplay.
'in' means one lot of letters goes inside another.
'times' becomes 'by' (both can mean 'multiplied by').
'older relative' becomes 'gran' (I've seen this before).
'by'+'gran'='bygran'
'bad' going around 'bygran' is 'BABY GRAND'.
(Other definitions for baby grand that I've seen before include "message of proud new parents?" , "Smaller piano" , "Infant piano?" , "Small, non-upright piano" , "Type of piano" .)