Will angels gather the elect at the end of this age?

Yes. Jesus told the disciples what to expect at the very end of the age, when those who are saved during Tribulation and survive (the elect, both gentiles and Jews) will be gathered together by His holy angels as the executors of His decrees.

"And He will send His angels with a great sound of a trumpet, and they will gather together His elect from the four winds, from one end of heaven to the other" (Matthew 24:31).

These angels will also gather out all things that offend and work iniquity.

"The Son of Man will send out His angels, and they will gather out of His kingdom all things that offend, and those who practice lawlessness, and will cast them into the furnace of fire. There will be wailing and gnashing of teeth."

Jesus' Parable of the Dragnet:

"Again, the kingdom of heaven is like a dragnet that was cast into the sea and gathered some of every kind, which, when it was full, they drew to shore; and they sat down and gathered the good into vessels, but threw the bad away. 49 So it will be at the end of the age. The angels will come forth, separate the wicked from among the just, and cast them into the furnace of fire. There will be wailing and gnashing of teeth" (Matthew 13:47-59)