It would be very nice to use a super telephoto for wildlife photography like the Canon 500mm f/4 or other long wonder. The problem with these lenses that most of us has not a budget to buy such a lens.
I thought about time as well. To make quality images often need to travel, which is not always possible, only perhaps several times a year. So if I combine the two and rent a lens for this special occasion can be a good solution.
The problem can be with renting that at most places actually you have to have the money of the lens price (as the caution), at other places they accept lower sum as a caution money.
You need to be very careful with the lens you intend to rent, not to break it, or someone cannot steal it, because then you are in trouble. It important to use companies, which you trust.
Check the lens carefully, when you get it, make some shots, check the pictures on computer, check nothing is broken, or scratched on the lens, if there is some problem you need to observe first. If there is some problem with the lens, better not to rent it, not having the problem afterwards, chose a copy which has no problem.
Why you rent something which is not actually good, and you don’t need ? On the other hand if you overlook some problem, they can count on you when you bring the equipment back.
If you very uncertain, you can try to rent a cheaper lens before, how is it going, how much does it actually cost, etc. The common trick in every trade in the VAT (value added tax). In Hungary it is 27%. It is important that the offer contains VAT, or you pay 27% (think your country rate) more than you expected.
Other thing needs to check is the schedule. Perhaps you need to fix date long before the lens need, in order to have it in the planned time.
Another good lens to rent is a macro lens, if you don’t have. Macro lens can broaden your possibilities considerably. You can make photos of insects, or water-drops, close-ups of flowers, interesting portraits, photos of eye, etc. You can make more artistic shots, because these lenses blur the background much more at closest distances.
It is important to prepare though, if you want to make insect pictures perhaps winter is not the best season. It is good to plan where you can find interesting critters, and not spend the time with searching when you pay for the lens.