Hi,
In System Preferences > iCloud (or Internet Accounts and the service you Use) the option for Contacts should be ticked.
On the iPhone in Settings > Mail, Contacts and Calendars > iCloud should then have Contacts with the slide across so it syncs.
If you don't use iCloud to do this then on the Mac in System Preferences > Internet Accounts you will have a service like Google for instance that also has an option to check the Contacts App to sync via the Google Address Book.
If this is the case then the account should be listed on the iPhone in Mail, Contacts and Calendars and you choose that rather than iCloud.
The Google for Instance is an example it could be Yahoo or Facebook or any account you have listed.
You can also check the Contacts app itself on the Mac.
Open the App and select the App Menu > Preferences > Accounts
Of the options listed only one should be active.
I suspect this is just a variation of what we have already seen.
7:49 pm Monday; November 30, 2015
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad