In a brief way Doctor Greig to distress (8)
I believe the answer is:
aggrieve
'distress' is the definition.
(I've seen this before)
'in a brief way doctor greig' is the wordplay.
'in' means one lot of letters goes inside another.
'a brief way' becomes 'ave' (abbreviation for avenue, a type of 'way'; 'brief' suggests a short form).
'doctor' is an anagram indicator.
'greig' with letters rearranged gives 'ggrie'.
'ave' going around 'ggrie' is 'AGGRIEVE'.
'to' is the link.
(Other definitions for aggrieve that I've seen before include "Distress, injure" , "Cause offence or injury to" , "Pain or injure" , "Cause to feel sorrow" , "Press heavily upon; distress" .)