I don’t know this piece. But here is my guess.
This is a song.
There are three staves, two for the piano accompaniment, and one for the voice.
If this is the case, a general principle with songs is that the piano does not play the melody – this is the responsibility of the singer.
You have two options.
1. Play the piano part as written and sing the melody. (That is sing the song and accompany yourself at the piano).
2. Rewrite the piece as a piano solo piece, so that the piano does everything and there is no singing. This is easier than it looks. Here is how you go about it: Copy the melody written the top staff on the treble staff. This means that you will have two “voices” (or parts) in a single staff. Use the 4th and 5th finger of the RH to play these melodic notes you just added to the treble staff. If this proves to be impossible, play some of the chords of the RH in the LH. If the notes are all over the piano, bring them closer by playing the melodic notes one octave lower. In short, distribute the notes between the hands as necessary. You may also simplify some of the chords by leaving notes out.
I hope this helps.
Best wishes,
Bernhard.