Not easy online this recent. Though you have looked around the cemetery, there may not have been a gravestone at all, so as you say not finding one doesn't mean he isn't buried there and you'd need to check the burial registers.
Okay, so first thing I did was check FreeBMD and there is a death registered in Q1 Northumberland North Second District for a James R W McLaren, aged 81. So that looks like his death registration and tells me where he died. UKBMD gives me the places covered by that registration district
https://www.ukbmd.org.uk/reg/districts/northumberland%20north%20second.htmlWhich is quite a long list and you need to bear in mind that, at his age, he may well have been living with a son or daughter who could have lived anywhere in the area and therefore may have been buried elsewhere in a civil cemetery or even in a churchyard (so you may need to check Parish burial records too)
A date and place of death, plus home address at time of death (if, for example he died in hospital) is very useful when searching for a burial - in any decade and in any register/newspaper/ database. A death cert from the GRO (or the slightly cheaper .pdf option) would give you that info. For me, the budget is limited and unless its my direct line I look for alternate sources of that info.
So I checked to see if there was a will or grant of administration for his estate (may/may not have been one) which would give me his exact date of death and, at that time, usually where he had been living, where he died and who did the probate/admin.
https://probatesearch.service.gov.uk/#willsUnfortunately there is no entry in the probate calendar for him - but its always worth a shot.
Then I checked the available online newspapers for the Alnwick area, to see if there is a death announcement which would mention funeral arrangements, but there isn't yet anything in the database for that area this recent. The only one they currently have for that decade is the Alnwick Mercury for 1950.
Another good source of free info is
https://www.gravestonephotos.com, which do have 80% of the existing gravestones in Alnwick in their database - but sadly no Mclarens
Alnwick Library may have old copies of the local papers if you can get there - I have no experience of either the local libraries or the archives at Woodhorn but others may help with info. The Woodhorn site has info on their holdings and details of what to expect if you visit and opening times. Research will most likely involve using a microfilm reader so I'd tell them in advance to ask them to reserve one if possible.
The Northumberland council site says on this page
http://www.northumberland.gov.uk/Registration/My-Northumberland-Wedding/Copy-certificates.aspx#searchingforgravesThat says if you are searching for a grave post 1900 to contact the cemetery you think they may be buried in - again a date and address would greatly help - though do be aware that there may be a charge and in some councils the charges can be hefty. Shy bairns get nowt though so email and ask. If they say there is a charge you don't have to proceed if its too expensive.
http://www.northumberland.gov.uk/Registration/Deaths/Crem.aspxcontact details are there.
Good luck with it, come back if you need further help.
Boo