In The Book Thief what is Papa's reaction when he discovers that Liesel has stolen another book? What does his reaction say about his character?

Papa, of course, is Liesel's endearing name for Hans, her foster father during World War II.  Unfortunately, you do not indicate which chapter (or larger part) of The Book Thief your question involves.  Please remember that Liesel steals nine books during the novel.  It is safe to assume, however, you do not mean her very first stolen book (The Gravediggers Handbook).  My best guess is you mean Hans’ reaction at the beginning of Part Three of The Book Thief, immediately after Liesel steals The Shoulder Shrug.  I will discuss Hans’ reaction to this book.  If your question refers to a different reaction from Hans, please repost your question.

In the case of stealing The Shoulder Shrug from the burning book pile, Hans’ reaction comes in stages.  First, his reaction when he sees the smoldering book and how it burned Liesel’s skin is to say, “What the hell do you call that?”  This is followed closely by, “Another one?”  This indicates a bit of surprise.  It also indicates that Hans knows exactly what Liesel is doing when she steals books.  However, it his next reaction that is more telling:

Looks like … I don’t need to trade any more cigarettes, do I?  Not when you’re stealing these things as fast as I can buy them.

This reaction says something very interesting about Hans’ character, namely that he supports Liesel in doing something illicit.  Hans, himself, acquires books in dubious ways (by trading cigarettes).  Liesel acquires books by “stealing” them. It is here that Hans has what the author calls a “revelation.”  His final reaction is the most interesting in that Hans says the following:

This is our secret, this book.  We’ll read it at night or in the basement, just like the others—but you have to promise me something. … If I ever ask you to keep a secret for me, you will do it.

It is this quotation that reveals the “revelation” that tells the most about Hans’ character.  Hans devotes himself here to two things:   keeping the secret and helping Liesel read.  Both of these devotions are against Nazi orders.  Hans also hints that there are more reasons he might need to hide information from the Nazis because Hans has secrets of his own. Therefore, Hans' reaction to Liesel stealing The Shoulder Shrug reveals much about his character.