Encrypt your ECDSA signature with NTRU to make them quantum secure, does that work?
So you want to encrypt the message's ECDSA signature with NTRU. 

Firstly, if the NTRU is secure against the quantum computers, then anything under NTRU encryption is secure against the quantum computers.

Secondly, NTRU has also digital signature, instead of ECDSA use NTRUSign.

Depending on different mathematical and computational problems are not considered a good practice. 

update: by the comments of Maarten Bodewes

Remember that, public key encryption and signature require two separate keys; public key and private key. In your case;


the public encryption keys generated by the receiver as $PK_{rec},SK_{rec}$ 
the digital signature keys are generated by the signer as $PK_{sign},PK_{sign}$.


As a result, the two public keys, $PK_{rec}$ and $PK_{sign}$, are generated by different people.