The phrase "a deep sympathy" is correct and usable in written English.
It can be used when expressing a strong feeling of compassion or understanding towards someone else's situation or emotions.
Example: "After hearing about her loss, I felt a deep sympathy for her and wanted to offer my support."
Alternatives: "a profound compassion" or "a strong empathy".
Bluemner painted out of a deep sympathy for Paterson's working class.
Not surprisingly, he grows up with a deep sympathy for the ladies who surround him.
Yet there was a deep sympathy, an underlying moral vision in her work.
"I feel a deep sympathy with the victims over this," said Michiaki Hatano, 30, a graduate.
Clark was driven by a sense of justice, a deep sympathy with crime victims, which sometimes led to emotional outbursts.
In response to Thoreau's journal entry dated April 11 , 1852— "It appears to be a law that you cannot have a deep sympathy with both man and nature.
It should bring a closer kinship, a better understanding, and a deeper sympathy for the wayfarers who must live a common life and die a common death.
In notes he wrote for himself (see Riemann Werke 1990: 539 Riemann said that he agreed with Herbart in matters of psychology and epistemology, but not ontology or with his ideas about the construction of the concepts of space, time, and motion. The disagreement masks a deeper sympathy.
I was happy that somebody kind of said, "Guys, what is this here?" But on the other hand, I have a real deep sympathy for black transgender women because they have it the hardest.
As well, the collection included "The Sea-Shell" and "Sailed", two poems in which Coolbrith described a woman's love with deep sympathy and an unusually vivid physical imagery, in a way that presaged the later Imagist school of Ezra Pound and Robert Frost.
Shortly before Mr. FitzGerald's death, Queen Elizabeth made a speech of reconciliation, expressing "deep sympathy" for "all those who have suffered as a consequence of our troubled past".
