is there such a thing as a one-way definition? A definition always looks something like this:

We say $P$ if and only if $Q$.

Is there an example of a definition where the biconditional is replaced with  "if" (and we mean just "if")? What about in the other direction?

Short answer: Every definition is a bi-conditional, but one direction is vacuous so we omit it for the purposes of logical aesthetic.
Long answer: Think about this in terms of what a definition is which is an assignment of meaning to a string of symbols. A string of symbols, say "$xyz$" has no inherent meaning unless we assign it one. So to say something like "A < something > is "$xyz$" if and only if < condition > " makes sense in both directions, but, because it is the first instance of "$xyz$" one direction in the statement ("< condition > $\implies$ "$xyz$" ") is vacuous because at that instance "$xyz$" means nothing in particular.
