A (subject) I have had -> un reloj que he tenido.

Ah I see I do not need to put lo as it has been explicitly said anyhow !

Sometimes people have corrected me by putting the time at the start, when would it be appropriate to do so?

It works like new -> functions como nuevo

Selling it for (quantity) -> use por

Thank you!

You can put the time at the start depending on what you're emphasising, what I meant in my comment is that the verb should be at the second position; it is not obligatory, but that is how natives usually build their sentences. This means you have two possibilities:
"Hace mucho tiempo me lo compró mi abuela."
"Me lo compró mi abuela hace mucho tiempo."
I don't know the context of the corrections you talk about, but the standard order is subject-verb-in/direct object-complements. "Hace mucho tiempo" is a complement of time, so it makes sense to put it at the end.
Bear in mind, however, that this order is not obligatory and is usually broken; in fact, when one complement breaks this order (which is very common), it is in most cases obligatory to put it between commas. You probably have noticed that by now in my corrections.
To summarize, the order can be changed in most cases depending on what you want to emphasise, but the verb should normally be at the second position.