My father passed away over 10 years ago and I never really got a chance to talk to him about his time served as I was too young and he didn't want to share. I have tried to do some reading on the UK's involvement in Cyprus but haven't had much luck as to understanding why he was there to begin with and what it would have been like.
Here are the photos I've found
Can't offer much but it looks like his cap badge is that of the Royal Green Jackets. From looking at Battalion deployments ( http://www.greenjackets-net.org.uk/assoc_new/regtl_history/bn_postings.htm ) it seems only 1st Battalion were posted there with the U.N. peacekeeping force around that time. My dad was also there in the 70's with the Light Infantry and from what he's told me, the majority of their time was spent along the Greek/Turkish border, mostly around Nicosia and Dhekelia. From the sounds of things, it was a fairly pleasant posting. Hope that goes a little way towards helping. You can always contact the Regimental Associations and see who remembers him and if they've got any stories to tell. If I can help with that, I'll try. I've got an uncle who served with the RGJ around that time.
Do you know what unit he was in? One line of enquiry would be to contact the existing Regiment, and ask if there’s any way your contact details could be passed along to his colleagues? This would not only answer your question, but also perhaps give you some great stories from people with whom he served. Good luck!