Begrudge having one left, one that's strong (9)
I believe the answer is:
resilient
'strong' is the definition.
(resilient can mean strong or tough)
'begrudge having one left one' is the wordplay.
'begrudge' becomes 'resent' (synonyms).
'having' means one lot of letters goes inside another.
'one' becomes 'I' (Roman numeral).
'left' becomes 'l' (common abbreviation).
'one' becomes 'I' (Roman numeral).
'i'+'l'+'i'='ili'
'resent' going around 'ili' is 'RESILIENT'.
'that's' acts as a link.
(Other definitions for resilient that I've seen before include "Flexible" , "Rebounding from impact" , "Able to bounce back from adversity" , "bouncing back" , "Elastic" .)