Performing around start of week is personal (3)
I believe the answer is:
own
'personal' is the definition.
('own' can be similar in meaning to 'personal')
'performing around start of week' is the wordplay.
'performing' becomes 'on' (I've seen this in other clues).
'around' indicates putting letters inside.
'start of' says to take the initial letters.
The first letter of 'week' is 'w'.
'on' placed around 'w' is 'OWN'.
'is' acts as a link.
(Other definitions for own that I've seen before include "Keep" , "Personal; possess" , "Posses" , "Possess - recognise - admit" , "Have in one's possession" .)