This stanza presents a question without an answer, but it does mention the response.

My Lord, what is it that Thou dost bestow?
The praise on this account fills up, and throngs
Eternity brimful, doth overflow
The heavens vast with rich angelic songs.
How should I blush? How tremble at this thing,
Not having yet my gam-ut learned to sing.

The introductory question, “What is that thou does bestow?” is not directly answered. The implied answer is, An engrafting of your life into my life, which results in you being brought into my web of relationships.

The rhythm of the first line puts the emphasis on the first word of the question, “What”. It does this by placing the word immediately after a pause and accented syllable. 

my LORD, WHAT is IT that THOU dost BEstow?

Yes, what is it? The rhythm makes it impossible to run past the question. 

It is now interesting that the question is not answered.  It is assumed by the word “this”

The praise on this account fills up, and throngs
Eternity brimful

But he never clearly says what “this” is.  He does raise the matter of relations again in the next stanza, “Thy graceful family”.  But here it is merely implied.

The result of this “this” is unceasing praise throughout heaven:

The praise on this account fills up, and throngs
Eternity brimful, doth overflow
The heavens vast with rich angelic songs.

In this, Taylor is again on solid scriptural ground. First, Taylor has come to a gathering:

Hebrews 12:22–23 (KJV 1900)

22 But ye are come unto mount Sion, and unto the city of the living God, the heavenly Jerusalem, and to an innumerable company of angels, 23 To the general assembly and church of the firstborn, which are written in heaven, and to God the Judge of all, and to the spirits of just men made perfect,

Second, the most common scene in the pictures of heaven is one of singing:

Revelation 5:8–14 (KJV 1900) 

⁸ And when he had taken the book, the four beasts and four and twenty elders fell down before the Lamb, having every one of them harps, and golden vials full of odours, which are the prayers of saints. ⁹ And they sung a new song, saying, Thou art worthy to take the book, and to open the seals thereof: for thou wast slain, and hast redeemed us to God by thy blood out of every kindred, and tongue, and people, and nation; ¹⁰ And hast made us unto our God kings and priests: and we shall reign on the earth. 

¹¹ And I beheld, and I heard the voice of many angels round about the throne and the beasts and the elders: and the number of them was ten thousand times ten thousand, and thousands of thousands; ¹² Saying with a loud voice, Worthy is the Lamb that was slain to receive power, and riches, and wisdom, and strength, and honour, and glory, and blessing. ¹³ And every creature which is in heaven, and on the earth, and under the earth, and such as are in the sea, and all that are in them, heard I saying, Blessing, and honour, and glory, and power, be unto him that sitteth upon the throne, and unto the Lamb for ever and ever. ¹⁴ And the four beasts said, Amen. And the four and twenty elders fell down and worshipped him that liveth for ever and ever. 

The picture of heaven being “brimful” and overflowing with song is remarkable. We normally do not picture songs as occupying a space, but here the songs are palpable. 

As is most common in Taylor, he pauses for a moment at the fact that he is not fit to be present in this company. Taylor’s treatise on the Lord’s Supper begins with a discussion of the scene in Matthew 25 of the man who is present at the wedding feast but lacks the proper garments. That image seems to lie behind Taylor’s unfitness which these preparations were met to remedy.

He says:

How should I blush? How tremble at this thing,
Not having yet my gam-ut learned to sing.

His gamut would be the full range music. The original usage from Gamma (the Greek letter) which in Medieval music was on tone lower than middle A + ut. The concept developed into the full range of musical notes which a voice or instrument could produce. In our modern usage, the origin in music has dropped out and now the concept is merely the full range. Here, Taylor has the musical usage in mind:

How can I possibly participate in this singing and not be ashamed – I don’t know how to sing with these angels.