Please please please suggest

 Sneha:

Cdramas where fl fall and chases first and get rejected by the ml..

• You Are My Glory
• Go Go Squid!
• A Love So Beautiful

 Sneha:

then fl totally gives up is when ml realizes his love for fl and chases back

I wouldn't say any of the dramas above fit this part exactly, but YAMG and ALSB have parts that are somewhat similar. 

 Sneha:

Cdramas where fl fall and chases first and get rejected by the ml.. then fl totally gives up is when ml realizes his love for fl and chases back. 

(Second lead couples prominent story also will do)

No wuxia , costume or historical dramas please...

Recent drama i saw

Fl chases ml

Itaewon class / roppongi class ( jdrama)   

Also for 2nd couple 

2nd couple from first romance and my girl ( both chinese dramas) 

I had watched few turkish dramas with this trope I'd recommend if u r interested

Lost Romance ..hidden gem ..loved it 

Begin Again

More and More Loves You (a toxic romance; and while she didn't chase him, she did fall first)

2nd Couple Prominent: (Edit: Misread your prompt. These 2nd couples are not Girl Chases Guy. They are just dramas with a really prominent second couple).

To Be a Brave One

Lucky's First Love

She and Her Perfect Husband

The Best of You in My Mind