Bishop leaves long note welcoming Eastern magistrate (5)
I believe the answer is:
reeve
'magistrate' is the definition.
(I've seen this before)
'bishop leaves long note welcoming eastern' is the wordplay.
'bishop' becomes 'b' (abbreviation used in chess).
'leaves' suggests deleting specific letters.
'long note' becomes 'breve' (I've seen this before).
'welcoming' is an insertion indicator (in sense of 'inviting in').
'eastern' becomes 'e'.
'breve' with 'b' taken away is 'reve'.
'reve' enclosing 'e' is 'REEVE'.
(Other definitions for reeve that I've seen before include "fasten rope" , "Pass a rope through a ring" , "Steward who told a Tale" , "Chief magistrate (hist.); pass (rope) through hole" , "Female flyer" .)