How does Shakespeare portray time as love's adversary in Sonnet 116?

The quote you have given could actually be used as the basis to discuss a number of Shakespeare's sonnets, which seem to place the passing of time in conflict with the beauty of the object of the speaker's affections and their love. However, famously, this poem seems to capture this conflict in its evocation of what "true love" should be in a relationship, pointing towards an eternal, unchanging sense of love that remains constant in spite of whatever damage time may do. Consider what love is said not to be, and then what it is said to be:

Love is not love
Which alters when it alteration finds,
Or bends with the remover to remove:
O no! it is an ever-fixed mark
That looks on tempests and is never shaken;

Love is therefore described as unchanging and not impacted by the changing landscape around it wrought by time. In particular, love is said not to be "Time's fool," even though beauty obviously comes under the power of time in the way that it fades so fast. Even though beauty and physical appearance may change thanks to the power of time, true love remains unchanged in the face of such decay:

Love alters not with his brief hours and weeks, 
But bears it out even to the edge of doom.

Note the way in which these lines place love in direct conflict with time, in the form of "brief hours and weeks." Thus, although this sonnet clearly places love and time in conflict, it is obvious that true love is never seriously threatened by the power of time, because true love is eternal and will carry on "even to the edge of doom." Whilst time has power over our appearance and age, true love renders such transformations as meaningless.

What is the relationship between time and love in Sonnet 116?

In Sonnet 116, Shakespeare declares the victory of love over time, even though time’s sickle cuts away beauty. Let’s look at this in more detail.

We often see time personified as an old man with a sickle. This symbolism emphasizes what will happen to all people as time passes. They age, and eventually they will be cut down in death. Time spares no one. Before death, time takes many things from people, including beauty and health.

Yet Shakespeare claims that love conquers time. True love remains no matter how much time passes and no matter how much the beloved changes as the years go by. Beauty is fleeting, but that does not matter to love. “Love’s not Time’s fool,” the poet declares. When love is real and strong, time cannot alter it. Love lasts all the way to eternity. Time can change much in human beings, and eventually, it can even bring death, but it cannot change love. The poet ends with the assertion that if he is mistaken about this, then no one has ever really loved.