Matthew 5:6 Blessed are they which do hunger and thirst after righteousness: for they shall be filled.
John 4:14 But whosoever drinketh of the water that I shall give him shall never thirst; but the water that I shall give him shall be in him a well of water springing up into everlasting life.
Ephesians 3:19 And to know the love of Christ, which passeth knowledge, that ye might be filled with all the fulness of God.
Philippians 3:8-10 Yea doubtless, and I count all things but loss for the excellency of the knowledge of Christ Jesus my Lord: for whom I have suffered the loss of all things, and do count them but dung, that I may win Christ, And be found in him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith: That I may know him, and the power of his resurrection, and the fellowship of his sufferings, being made conformable unto his death;
Reading from these verses we might gain insight into the use of hunger and thirst as it pertains to righteousness. While hunger and thirst are words we relate to in matters of the flesh, it is flesh that consumes and requires replenishment. Not so in the Spirit and His righteousness, it does not consume but is rather a never ending source of righteousness and more.
Romans 10:4 For Christ is the end of the law for righteousness to every one that believeth.
While the cross put an end of the law for righteousness sake, Christ is more than just righteousness.