Can I graft something edible onto this tree?

Hi all, this is my first go at starting a thread so hopefully I am in the right place! I have a relatively small garden with an established ornamental tree in it. I think it might be Prunus cerasifera (Nigra?) but it has never bore fruit.

I would love to grow some tree fruits (ideally apple but if it is what I think plum seems like a better choice) and was hoping it might be possible to graft something onto the tree that I already have.

I have attached (not great quality but all I have) pictures to help with ID. In the picture of the full tree it is hidden a bit by a neighbours tree coming through the fence, mainly included it to show size (it's been trimmed a bit since this picture to around 14 feet tall).

I would welcome any follow up questions (I will try to answer!) and/or advice. :)

You can graft another plum onto that -- it's best to pick one that is a good pollinator match if you can, the the remaining branches may start fruiting better.  
To graft, select one of the large branches and cut it, then do a "cleft graft" with another variety.  

The lack of fruit may be from the variety (some ornamental plums are more flowering than fruiting), the pollination availability (if nothing compatible is nearby) or just the season and conditions (too cold and rainy for the bees when it flowers)

The grafting part needs a lot more detail than what I outlined, but it will be a fun project if you can research your way through it.

Eric Thompson wrote:You can graft another plum onto that -- it's best to pick one that is a good pollinator match if you can, the the remaining branches may start fruiting better.  
To graft, select one of the large branches and cut it, then do a "cleft graft" with another variety.  

The lack of fruit may be from the variety (some ornamental plums are more flowering than fruiting), the pollination availability (if nothing compatible is nearby) or just the season and conditions (too cold and rainy for the bees when it flowers)

The grafting part needs a lot more detail than what I outlined, but it will be a fun project if you can research your way through it.

Thanks for your reply Eric! This is the first place I've lived that has any trees so I've plenty of research to do! You have given me a lot to think about, as the only other fruit 'tree' nearby is some sort of wild currant bush. In the two years we have lived here the tree has flowered before/around our last frost date so perhaps too early for pollinators. It is also Scotland, and my area typically has over 250 rainy days each year!

I still think it's worth a bash though so I will be trying to figure out what varieties might be a suitable match and then go from there, thank you! :)