1. Partner-3 has to obtain court order seeking succesion rights on share of deceased Partner-1. Without this partner-3 being only 15% stake holder CANNOT dictate ANY terms & conditions.

2. Partner-2 & Partner-4 can continue operating their business or buy-out the entire business with its Assets, Liabilities & Good-Will etc.... by settling on an amicable amount with the legal heirs of Partner-1.

3. A Civil Court case also can be filed, by raising a dispute and a stay order can be obtained on partner-3, in affect arm-twisting into a amicable settlement.

under Section 42 of the Partnership Act it is provided that "subject to contract between the partners, a firm is dissolved-(c) by death of a partner."

2) It is evident that this particular provision is .subject to the contract between the partners. Where the contract between the partners contemplates expressly or impliedly that the death of a partner would not result in dissolution of the partnership firm, the said term in the contract is to be given effect to superseding the provision contained in Section 42(c).

3) the value of the assets should be ascertained in order to reimburse the heirs of the deceased partner in the shape of money

No remedy except as per partnership deed. Surviving partners can continue the business/firm, no new deed will execute except resolution by majority partners. If 3 dose not want to continue can resign as per partnership deed but cannot force to dissolution and sale of business. 

On death of partner, his legal representative are entitle to profit as per the share in partnership otherwise firm will dissolve, properties will partition as per contribution and can form fresh deed with same or other name with 2 and 4 properties.

A partner of a firm may not be dismissed from a partnership firm by a majority of the partner except in exercise, in good faith, of powers conferred by contract between the partners.

All the partners can expel him as per provision of law. But he can later challenge the expulsion in court

See since partner one died the legal heirs of partner cab seek there share or can give you option to purchase there share or dissolve the business. See in case they are not ready the business needs to be dissolved.. 

You and 2nd partner cannot expel him if he is not ready the firm needs to be dissolved.

You have to enter into a new partnership deed to aquire the business of the existing firm and pay the valuation of the firm to the individual legal hairs of p1 and shares of p3.

In case the amount can not be paid after dissolution of firm that may be taken as loan from him if agreed.

In other case the firm will dissolved by the court if a partnership dispute arise.

As you people are in majority you should ask him to sell his business or be a silent partner.

In the event of any disputes an arbitrator can be appointed for the resolution of the dispute.

the partnership deed plays a important role as generally the partnership deed contains a clause that in the event of death of one parter what will happen to the assets of the firm . So I need to know that whether you have such a clause in your deed so that your query can be answered more efficiently.

You go through the partnership deed or articles of association of the company.

You can take action as per the conditions and terms contained in the deed in this regard.

You do not have to accept his terms under any pressure.

You can ask him to proceed as per law.

1. Partner 3 can be expelled from partnership firm under section 33 of Indian partnership act 1932 

2. Section 33: Expulsion of a partner

There are various reason why a partner may be expelled from a partnership firm. A partner of a firm may not be dismissed from a partnership firm by a majority of the partner except in exercise, in good faith, of powers conferred by contract between the partners.

3. It means that he can be expelled if you have clause for expulsion in your partnership deed but he will be treated as retired partner of firm.