Short answer. Yes, but only at the court's discretion. Rule 132, Section 7 primarily allows redirect examination to explain or supplement answers given during cross-examination, but it also states that "questions on matters not dealt with during the cross-examination may be allowed by the court in its discretion." New topics aren't guaranteed, but they're not barred either.
What the law says
After the cross-examination of the witness has been concluded, he or she may be re-examined by the party calling him or her to explain or supplement his or her answers given during the cross-examination
Rule 132, Section 7 — Re-direct examination; its purpose and extent. Read the full provision →
What the law says
On re-direct examination, questions on matters not dealt with during the cross-examination may be allowed by the court in its discretion
Rule 132, Section 7 — Re-direct examination; its purpose and extent. Read the full provision →
The primary purpose of redirect examination
Rule 132, Section 7 states the main function of redirect first: "After the cross-examination of the witness has been concluded, he or she may be re-examined by the party calling him or her to explain or supplement his or her answers given during the cross-examination." Redirect is built primarily around clarifying or adding to what already came out on cross, not around opening entirely fresh ground.
The specific allowance for new matters
The same section then addresses your exact question: "On re-direct examination, questions on matters not dealt with during the cross-examination may be allowed by the court in its discretion." So the rule does not confine redirect strictly to what was raised on cross — it expressly contemplates questions on matters the cross-examination never touched, as a distinct possibility from the explain-or-supplement purpose described in the first sentence.
Why this is the court's call, not an automatic right
The phrase "may be allowed by the court in its discretion" is permissive, not mandatory. Bringing up an entirely new topic on redirect is not something your lawyer can simply do as of right the way explaining or supplementing cross-examination answers is described — it is something the court has to actually permit, and the court retains discretion over whether to allow it in a given case, weighing the circumstances as they actually stand at that point in the trial.
What this means for your lawyer's questions
In practice, this means your lawyer can ask the court to allow questions about matters the cross-examination never raised, and the rule gives the court a real basis to say yes. But because the allowance is discretionary, your lawyer cannot assume in advance that any new topic will be permitted; the court's willingness to allow it, in your specific case, is what will actually decide whether that line of questioning goes forward on redirect, rather than any entitlement written into the rule itself.