If you have not divorced your wife thrice and both are ready to live like husband and wife then only new nikah is enough. You should do new nikah in the presence of Shariah witnesses. There is no need of halalah. Your nikah is valid within iddah and after iddah as well. Yes, if three talaqs have taken place then nikah will not be valid without a Shariah halalah.
Allah knows Best!
Darul Uloom Deoband