I do not think that there should be an apostrophe....but I'm not sure what your sentence is.
Can you write it out in full without the apostrophe and I'm sure loads of people will be able to tell you.
If you meant to add something such " after 33 years' service I have decided to retire'" then yes, you need an apostrophe.
One way to check is to imagine if it was one year. To say "one year service" would sound odd; "one years service" would sound right but would clearly be wrong; so that leaves "33 years' service"- service of 33 years
No expert but I would doubt it. I can't see it would stand for something missing and as possessive does English allow a year to own something ? I think 5 years owns its own length but I doubt the rules allow it.
sorry about this guys, seem to have a gremlin in my computer - the full question should read.......If I want to write the sentence >>>>>'We will offer up to two years accredited and non accredited training programmes that can include'
I say YES it should have an apostrophe, given that if the requirement was one year you wouldn't write one year or one years- you'd have to say one year's accredited service.
But if in doubt, change the sentence round accredited service of two years
No tsure I agree about the apostrophe, FF, but I do agree that wording the sentence differently would be better all round.
We will offer training programmes of up to two years, accredited and non-accredited.