The key is to play to your strengths, rather than focus on the weakness.
Then, it makes sense to imagine a manner in which the exceptionally low intelligence manifests itself, but that's mostly to give your character some personality. For example, perhaps he gets confused easily when people are talking fast, using big flowery words, etc. He likes to mull things over in his "slow mind". Maybe he tends to repeat cliches that sound like wise advise, and he bases his life around those principles, usually following them quite literally rather than abstracting them to general situations or understanding the nuance of when they apply and when they don't apply. In fact, a major character development may occur when he DOES see how advice like "look before you leap" applies in a situation in which he is not actually about to physically leap. But this manifests as insight, rather than intelligence, thus further enhancing his general wisdom.
With high Wisdom, you want to play to that strength by having proficiency in as many Wisdom-based skills as possible. So, let's say you have proficiency with the Insight, Perception, and Survival skills, and the following non-combat encounter occurs:
Your party is chasing an NPC who escaped in the previous encounter. They get to a crossroads where they meet an old crone. The Bard (Charisma-based) PC starts chatting her up, asking about whether they've seen the NPC you're after. The Wizard (Intelligence-based) is making Arcana checks to figure out if the crone is some creature he recognizes and what are it's weaknesses. The crone is saying that the NPC went "thataway" pointing down the road heading to the east.
Meanwhile, your cleric is getting confused by all of the talking. It's giving him a headeache. He gives his face a rub to try and mute the talky talky. Then he studies the crone for a moment. Ignoring her words, he listens more to the sound of her voice, the way her words trail off. He studies her body language, her facial expressions and gestures. He doesn't like her - she makes him feel icky - and he doesn't trust her. (Insight)
Losing interesting in the conversation, he glances around, and notices something a few feet down the road to the west. (Perception)
While the loud talky talkies keep making their noise, he wanders off in that direction. Taking a closer look, he notices footprints that match the quarry and determines that the NPC went in this direction. (Survival).
"She's lying," he whispers to himself. Then he turns to his companions and says in a louder voice: "She's lying." Without further explanation (words aren't his strength), he turns and wanders off down the road to the west, eyes down as he follows the tracks of his quarry.
The party can ignore him for his stupidity, or learn to trust his instincts. That's their choice, but you have the agency to make your character into whatever you want - the ability scores are a suggestion for what will be more successful.
When it comes to making a cleric, consider what the scores mean. In my experience with religious communities, there tend to be those who are academically inclined - e.g. reading the bible regularly and contemplating what it means for their lives - and those who are more faith-based - often devout without ever spending much time reading the bible. Your cleric would fall toward the extreme end of the spectrum on the faith-based side. Perhaps he had a spiritual encounter and "just knows" what his chosen god would want him to do in most situations. He prays out of pure faith and he follows the most basic tenets of the faith literally and religiously. Perhaps this is exactly what his god favours in him - faith and obedience rather than pontification and second-guessing the will of the gods. And he is rewarded with supernatural powers.
Anyway, there's plenty of room for action rather than sitting in a corner.
To me, high Wisdom suggests "I have a hunch" in non-combat situations; the low intelligence just reinforces this as the only real method of solving problems, rather than combining it with something like Investigation.