With Harrison out, Jung-Ho Kang will, presumably, take over at third. That doesn't seem so bad -- Kang can handle the position defensively, and he's actually out-hit Harrison this year, although he's come back to earth in the past six weeks or so. The Pirates can mostly replace the 2015 version of Harrison in their lineup. Where this will hurt the Pirates is their depth. Their bench had already been a problem, with Chris Stewart and Kang the only current members of the Bucs bench who had shown they could handle their share of the load.
Luckily, the Pirates are entering trade season. They don't necessarily need another infielder, but they really could use someone on their bench who can hit.
Speaking of which -- well, sort of -- the Bucs will place Harrison on the disabled list to clear space for the newly acquired Travis Ishikawa.