The cleric would not need to make a saving throw
The warding bond spell says:
While the target is within 60 feet of you, it gains a +1 bonus to AC and saving throws, and it has resistance to all damage. Also, each time it takes damage, you take the same amount of damage.
The cleric will suffer only the damage (halved) that the paladin receives from the wereboar. The curse is not damage, so warding bond does not transfer that to the cleric.
From the wereboar's Tusks action:
If the target is a humanoid, it must succeed on a DC 12 Constitution saving throw or be cursed with wereboar lycanthropy.
Here "it" refers to "the target", which was the paladin in this case. The cleric is not the target, and the damage (and only the damage) is only transferred because of warding bond (i.e. the cleric is not a target of the attack, they are effectively being damaged by their own spell).
So the cleric would not need to make a saving throw, as they are not the target of the lycanthropy curse.