Sadly fredkins If roomful were the answer to 3d it would put a u in 13a. Besides the h(4th letter is definitely right) and i believe nowhere looks right
so 13a is ?E?R?.
A possible but tenuous explanation of "Peter"as the answer here.
Double meaning.
Peter the name of the first Pope.
Peter in bridge and whist,is a signal to ones partner indicating one has a short suit,by playing a high card followed by a low card.The "better" could be a reference to the playing these card games for money.
Is this crossword from "The Tablet"?