Krishna speaks4.15

एवं ज्ञात्वा कृतं कर्म पूर्वैरपि मुमुक्षुभिः।कुरु कर्मैव तस्मात्त्वं पूर्वैः पूर्वतरं कृतम्॥

evaṃ jñātvā kṛtaṃ karma pūrvair api mumukṣubhiḥkuru karmaiva tasmāttvaṃ pūrvaiḥ pūrvataraṃ kṛtam

Word by word
evam: thusjñātvā: knowingkṛtam: performedkarma: actionspūrvaiḥ: of ancient timesapi: indeedmumukṣubhiḥ: seekers of liberationkuru: should performkarma: dutyeva: certainlytasmāt: thereforetvam: youpūrvaiḥ: of those ancient sagespūrva-taram: in ancient timeskṛtam: performed

The verse says

Knowing this, people long ago who wanted to be free still did the work. So do the work - the way it was done before you, long before.

In plain words

The conclusion, and it is an instruction to copy.

The ones who wanted liberation - mumukṣubhiḥ - did not stop working. They understood this and kept going.

And then the odd, doubled phrasing: pūrvaiḥ pūrvataraṁ kṛtam - done by the ancients, done still earlier.

Where you've felt this · in family life

You hold a cricket bat exactly the way your father showed you, and he held it the way his coach did in 1974. Nobody in that chain ever sat down and proved it was the best grip. It kept working, so it kept being handed on.

Going deeper

The doubling at the end is not clumsy. Pūrvaiḥ pūrvataram - by the ancients, more anciently still - pushes the precedent back past the reach of the sentence.

It is the same move the chapter made with whenever, whenever and age after age. Repetition is being used to stretch time, and the effect is to make the practice older than any account of it.

What is claimed is that people seeking release historically did not withdraw. Mumukṣu is the technical word for someone whose aim is exactly that, and the Gita says those people worked.

That is the argument of Chapter 3 arriving with a lineage attached. First it was made structurally: you cannot stop, so the question is how. Now it is made historically: the ones who got there did it this way.

And it closes the loop with the chapter's opening. Verse 1 traced a chain of transmission. This verse says the chain was not carrying a doctrine to be believed but a way of working, and hands it to Arjuna as something to do.