See this is your first post on the site, if no one else does welcome to the board.
OK it looks as if the timber and boards are sound, no rot, which indicates the old shower seal and tiling were doing their job correctly.
As for "Patching up" the gap yes you can.
A couple [or three]of things.
1/. Try to keep the tray away from the boarding you are going to put in, not by much, just a wee bit. Depending on the dimensions of the tray you can if you want take the boarding either down to the tray or down to the floor.
2/. If it were me I would seal the resulting gap in 1/. above with mastic.
3/. Keep the tiles away [as above] from the tray, this to prevent the thermal differences between tile and tray from affecting each other, especially the tiles, they can be blown off by thermal differences if the tile touches the tray.
If you need to find a tradesperson to get your job done, please try our local search below,
or if you are doing it yourself you can find suppliers local to you.
Select the supplier or trade you require, enter your location to begin your search.
Please select a service and enter a location to continue...
Are you a trade or supplier? You can create your listing free at DIYnot Local