It seems like you're facing an issue with the timing chain tensioner. The noise you hear when starting up is probably caused by a worn tensioner or guide. This problem is pretty common, especially with the VQ40DE engine found in the Frontier
To resolve it, you'll want to replace the worn-out parts, like the tensioner and guides. Keeping up with regular oil changes can help avoid sludge buildup, which might block the tensioner. If you're not sure, it's a good idea to get a mechanic to take a look, since ignoring it could lead to more serious damage
As for the costs, they can vary, but generally, you can expect a shop to charge between $1,200 and $1,400 for the repair
For a comprehensive guide on replacing the timing chain, you might find this video helpful: