Something like this should work:
DECLARE @Today date = GetUtcDate();
DECLARE @MonthStart date, @YearStart date, @YearEnd date;
SET @MonthStart = DateAdd(month, DateDiff(month, 0, @Today), 0);
SET @YearStart = DateAdd(month, 7 - Month(@MonthStart), @MonthStart);
If Month(@MonthStart) < 7 SET @YearStart = DateAdd(year, -1, @YearStart);
SET @YearEnd = DateAdd(day, -1, DateAdd(year, 1, @YearStart));
WITH EmployeeAdvance As
(
SELECT
EmployeeId,
Count(1) As NumberOfAdvances
FROM
AdvancePayment
WHERE
RequestedOn Between @YearStart And @YearEnd
GROUP BY
EmployeeId
)
SELECT
E.EmployeeId,
E.FullName,
CASE
WHEN A.NumberOfAdvances > 1 THEN 'Not Eligible'
ELSE 'Eligible'
END As Status
FROM
Employee As E
LEFT JOIN EmployeeAdvance As A
ON A.EmployeeId = E.EmployeeId
;