All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
According to the general rule, participation in the capital of a partnership should be in cash paid by partners based on their contribution and that the capital is mixed factually or constructively and that both parties enjoy the right of disposal as agreed between them. This is because a partnership contract is based on representation (Wakala); meaning that each partner is a representative of the other concerning the right of disposal. An-Nawawi said: "Partner`s right of disposal is that of an agent." {Rawdat W Umdat Al-Mufteen, Vol.4:p.283}.
It is allowed that a new partner joins an existing partnership; however, this is provided that the original partners approve of that and that the capital is turned into cash to determine the value of each partner's contribution and to calculate the profit and loss ratio accordingly. Speaking about the partnership contract, An-Nawawi (May Allah have mercy on him) said: "Profit and loss is incurred in accordance with the contribution of each partner in the capital." {Menhaj At-Talibeen, p.132}. I.e. each according to their share. However, if a partner or other led to company`s loss due to negligence and misconduct, then they have to make compensation.
In conclusion, it is allowed in Sharia to introduce a new partner into an already existing partnership functioning in car trading; however, this is provided that all partners approve of that and the pervious Sharia conditions of partnership are fulfilled. And Allah the Almighty knows best.