There will be different opinions on this. Some will tell you the deity should be completely changed, others will say it isn't so important, and devotion is more important. Ancient temples such as Lingaraj in Bhubaneswar worship a shivalinga that was shattered into many pieces by invading muslims. In Kantilal the ancient deity of Nila Madhava has his face disfigured (smashed) also by invading muslims. Still the worship continues, because the deity is not only based on the physical shape of the stone. It's the worship and spiritual potency that really matter.

There are rituals for changing a deity if it is absolutely necessary, but it shouldn't be done with ancient deities, as the priests may not have the potency to transfer the built up spiritual power of thousands of years of worship.

In your case, if it is a home deity, you can continue worshipping it as is. For Nila Madhava deity in Kantilal, they place a spot of chandana paste on the broken area.