Avatar of an avatar, such a precept did not exist in Hinduism. Lord Krishna is himself an avatar of his era, a savior messiah. In the entire history of mankind Lord Krishna can be considered the first avatar who truly manifest on mother earth to save mankind in times of extreme strife, tribulation.
Avatar in Hinduism stood for an enlightened one like Mahavira; Gautama Buddha even Jesus Christ or Prophet Mohammed coupled with powers of Chanakya (the best administrator in the entire history of mankind). To save lives of millions of countrymen and soldiers Chanakya got 100 kings eliminated in one night.
The might of an avatar cannot be conceptualized, it has to be witnessed.
When the society takes a downturn, reaches its lowest ebb advents an avatar to re-establish Dharma (righteousness) against evil forces of adharma (lawlessness)!
To cleanse the society of its ills advent of an avatar announces precipitation of a mother of all wars. In Dwapar Yuga in times of Lord Krishna mankind witnessed battle of Mahabharata, which was aptly titled War of Dharma.
Even in present times, the present Kali Yuga mankind awaits advent of Kalki avatar, a one-man army who shall unveil himself at the opportune moment. It is at this moment mankind would witness precipitation of world war 3, a man-made calamity, a gigantic calamitous full-scale nuclear war.
The advent of an avatar gets necessitated to provide a soothing balm, assuage the hurt feelings of the community in the aftermath of war of Mahabharata magnitude. As detailed in Hinduism scriptures every 3500 to 5000 years advents an avatar to re-establish Dharma (righteousness).