Rector in church suspended about half of LP record (9)

I haven't cracked this one yet — but the brilliant team at Fifteensquared have:

R (abbreviation for rector), in CH (abbreviation for church) + ON ICE (suspended = delayed or held in reserve), around the first half of L [p]. Though I can’t help thinking that “half of a two-letter abbreviation” is a rather odd way to clue a single letter. Chronicle = a historical record of events.