This guy finishing what was once your herb (5)
I believe the answer is:
thyme
'herb' is the definition.
(I know that thyme is a type of herb)
'this guy finishing what was once your' is the wordplay.
I cannot really see how this works, but
'your' could be 'thy' ('thy' historically meant 'your') and 'thy' is found in the answer.
The remaining letters 'me' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...
Can you help me to learn more?
(Other definitions for thyme that I've seen before include "Kind of mint" , "Culinary adjunct" , "Small shrub: leaves used to season food" , "Part of song: ''parsley, sage, rosemary and . . . . .''" , "Aromatic shrub" .)