if there is side play.. beairng is going... this will hog the seal out, and if allowed to go out will cause other problems... if no thrust play yet.. just wait.
if there is thrust play, could be bearing going. or could be slipepd seal wear ring. or could be broke split ring, or could be popped out split ring, or could be damaged bearing carrier.
Take yer pic. any of those can cause the pto shaft to walk out of engagement. A bad detent could do it too , thru vibration..e tc... I've seen more broke split rings than bad detents... just sayin..
Now. if the split ring popped out.. you may or may not be able to just pop back in and go. sometiems the bearing carrier is visibly damaged with a ridge of metal removed so there is no land for the ring left. other times there is just an edge removed where the ring shoved out.. and while it may hold a bit.. it will push out easier next time... sometiems you are just living right and you put it back in and it's fine..
causes for this can be that the telescoping pto shaft on a mower, etc was either too log so that when collapsed it shoved the tractor pto stub into the bearing carrier, .. or that the shafts were rusted and when it needed to extend, instead it tugged on the pto stub. either will pop snap rings.
gain. bearing could be worn and allow the play.
shaft passes thru hyds and diffy sump.. so drain both to pull shaft.
4 bolt job and should slide right out. be carefull removing it and reinstalling. as said there is a mid sump seal.. so try to support the shaft going in and coming out so you don't hog the seal out.. they usualy leak a bit anyway.. but if you pop the lip.. it will allow mixing straight thru.. most people use utf in both sumps due to this.
once you pull here.. it is a 15m job to pull split rings.. drop bearing carrier off shaft assy, drive seal out. clean.. inspect.. reseal.. reseat wear ring if needed, if it moved, inspect bearing.. etc.
reassemble.. and clean gasket surface. regasket and go.
replacing the bearing and wear ring would add another 10m maybee.. or less if you've done 20 of them.. etc..
now the complications.
1, do check the detend.. if should be somewhat positive. if it's sloppy. fix that too.
2, if it has been allowed to walk out of engagement often / for years. the splines and couple will wear and not play nice together at some point.. requiring a front of rear end split.. walking out of engagement is bad. you may have seen some people bunji a pto selector in. this is a bandaid.. but at least keeps a shaft from walking out even if it is way out of spec on thrust paly. IMHO.. a bunji to hold one in, is only to finish that dayus mowing after that. pull and fix or don't use it.
post back if you hit a snag.