A.T. Robertson Commentary John 13:34

"A new commandment I give unto you, that ye love one another; even as I have loved you, that ye also love one another." — John 13:34 (ASV)

New (καινην). First, in contrast with the old (αρχαιος, παλαιος), the very adjective used in 1 John 2:7) of the "commandment" (εντολην) at once called old (παλαια). They had had it a long time, but the practice of it was new. Jesus does not hesitate, like the Father, to give commandments (15:10,12).

That ye love one another (ινα αγαπατε αλληλους). Non-final use of ινα with present active subjunctive of αγαπαω, the object clause being in the accusative case in apposition with εντολην. Note the present tense (linear action), "keep on loving."

Even as (καθως). The measure of our love for another is set by Christ's love for us.