Shukla Yajurveda Book III
We call the spirit hither with a hero-celebrating strain, Yea, with
the Fathers’ holy hymns (53)
The spirit comes to us again for wisdom,
energy, and life, That we may long behold the Sun (54)
The spirit here denotes Atma which comes to us (human beings) after being somewhere for sometimes. Since it is clearly written that it comes again, it clearly denote reincarnation.
Atharva Veda IX.10
Back, forward goes he, grasped by power inherent, immortal born the
brother of the mortal. Ceaseless they move in opposite directions: men
mark the one and fail to mark the other (16)
The he mentioned here is Atma which is immortal and the mortal here is body. What this verse says is that there is no time frame for reincarnation. It also says men will notice only one thing (mortal body) and fail to notice the other (Atman).
Rig Veda X.16
Burn him not up, nor quite consume him, Agni: let not his body or his
skin be scattered. O Jātavedas, when thou hast matured him, then
send him on his way unto the Fathers. (1)
When thou hast made him ready, Jātavedas, then do thou give him over
to the Fathers. When he attains unto the life that waits him, he shall
become the Deities' controller. (2)
These verses pray to Agni to send the spirit of the dead person to forefathers once the body is perfectly burned up.
The Sun receive thine eye, the Wind thy spirit; go, as thy merit is,
to earth or heaven. Go, if it be thy lot, unto the waters; go, make
thine home in plants with all thy members.(3)
The merit mentioned here is Karma. What this verse says is that based on the merit, the spirit of the dead person go to earth (to be born as human) or heaven or waters. ( I don't know what the waters here signify)
Again, O Agni, to the Fathers send him who, offered in thee, goes with
our oblations. Wearing new life let him increase his offspring: let
him rejoin a body, Jātavedas. (5)
This verse asks Agni to send the dead person to forefathers(Pitrus) through the oblations or last rites done by some people. Also the second sentence clearly says he may be reborn by joining a body and increase his offspring.