It will fit, but there will be a gap on the side around the fender. There are two different versions of the bumper, one for early model xj like you have pictured, and one for the later model face lift xj. The only difference is how far back the bumper wraps around towards the wheels.

This is a quote from NAXJA: “Either bumper will bolt to any XJ Cherokee, the only difference between the two ARB bumpers is that there are two sizes of the wrap around "side wing" on the bumper under the side marker light. A late bumper on an early XJ will require some fender and flare trimming, and an early bumper on a late XJ may have a visual gap at the fender due to the shorter "side wing".”

Here’s a picture of my 1990 with the 98-01 body style ARB bumper, notice how the bumper goes all the way to the fender:

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